Predicting Spontaneity at Different Temperatures: Worked Examples

🧪 Quick Study Guide

• 🌡️ Temperature's Role: Temperature significantly influences spontaneity. Reactions can be spontaneous at one temperature but non-spontaneous at another.
• ⚛️ Gibbs Free Energy: The Gibbs Free Energy ($G$) determines spontaneity. The equation is: $G = H - TS$, where $H$ is enthalpy, $T$ is temperature (in Kelvin), and $S$ is entropy.
• ➕/➖ Spontaneity Criteria:
  • If $G < 0$: The reaction is spontaneous.
  • If $G > 0$: The reaction is non-spontaneous.
  • If $G = 0$: The reaction is at equilibrium.
• 🧮 Calculating $\Delta G$: Often, we calculate the change in Gibbs Free Energy ($\Delta G$) using: $\Delta G = \Delta H - T\Delta S$.
• 📝 Enthalpy ($\Delta H$): Represents the heat absorbed or released during a reaction.
• 🌀 Entropy ($\Delta S$): Measures the degree of disorder or randomness in a system.
• 💡 Temperature Dependence:
  • If $\Delta H < 0$ and $\Delta S > 0$: The reaction is spontaneous at all temperatures.
  • If $\Delta H > 0$ and $\Delta S < 0$: The reaction is non-spontaneous at all temperatures.
  • If $\Delta H < 0$ and $\Delta S < 0$: The reaction is spontaneous at low temperatures.
  • If $\Delta H > 0$ and $\Delta S > 0$: The reaction is spontaneous at high temperatures.

✍️ Practice Quiz

1. Question 1: For a reaction with $\Delta H = -100 \text{ kJ/mol}$ and $\Delta S = -50 \text{ J/(mol⋅K)}$, below what temperature will the reaction be spontaneous?
   1. 2000 K
   2. 20 K
   3. 2 K
   4. 200 K
2. Question 2: A reaction has $\Delta H = +50 \text{ kJ/mol}$ and $\Delta S = +100 \text{ J/(mol⋅K)}$. Above what temperature will the reaction be spontaneous?
   1. 500 K
   2. 0.5 K
   3. 50 K
   4. 5 K
3. Question 3: If $\Delta G$ is equal to zero, the reaction is:
   1. Spontaneous
   2. Non-spontaneous
   3. At equilibrium
   4. Impossible
4. Question 4: Which of the following conditions will ALWAYS result in a spontaneous reaction?
   1. $\Delta H > 0$ and $\Delta S > 0$
   2. $\Delta H < 0$ and $\Delta S < 0$
   3. $\Delta H > 0$ and $\Delta S < 0$
   4. $\Delta H < 0$ and $\Delta S > 0$
5. Question 5: For a certain reaction, $\Delta H = -50 \text{ kJ/mol}$ and $\Delta S = +25 \text{ J/(mol⋅K)}$. What can be said about the spontaneity of the reaction?
   1. Spontaneous at all temperatures
   2. Non-spontaneous at all temperatures
   3. Spontaneous only at high temperatures
   4. Spontaneous only at low temperatures
6. Question 6: A reaction is spontaneous at high temperatures but non-spontaneous at low temperatures. What are the signs of $\Delta H$ and $\Delta S$?
   1. $\Delta H < 0$ and $\Delta S < 0$
   2. $\Delta H > 0$ and $\Delta S > 0$
   3. $\Delta H < 0$ and $\Delta S > 0$
   4. $\Delta H > 0$ and $\Delta S < 0$
7. Question 7: What is the value of $\Delta G$ at equilibrium?
   1. $\Delta G > 0$
   2. $\Delta G < 0$
   3. $\Delta G = 0$
   4. $\Delta G = 1$